Journal of Animal Ecology 2014

doi: 10.1111/1365-2656.12315

Density-dependent movement and the consequences of the Allee effect in the model organism Tetrahymena Emanuel A. Fronhofer1*, Tabea Kropf2 and Florian Altermatt1,3 € Department of Aquatic Ecology, Eawag: Swiss Federal Institute of Aquatic Science and Technology, Uberlandstrasse 2 133, CH-8600 Du€bendorf, Switzerland; Department of Environmental Systems Science, ETH Zu€rich, CH-8092 Zu€rich, Switzerland; and 3Institute of Evolutionary Biology and Environmental Studies, University of Zurich, Winterthurerstrasse 190, CH-8057 Zu€rich, Switzerland 1

Summary 1. Movement and dispersal are critical processes for almost all organisms in natural populations. Understanding their causes and consequences is therefore of high interest. While both theoretical and empirical work suggest that dispersal, more exactly emigration, is plastic and may be a function of local population density, the functional relationship between the underlying movement strategies and population density has received less attention. 2. We here present evidence for the shape of this reaction norm and are able to differentiate between three possible cues: the relative number of individuals, the presence of metabolites (chemical cues) and resource availability. 3. We performed microcosm experiments with the ciliate model organism Tetrahymena in order to understand the plasticity of movement strategies with respect to local density while controlling for possible confounding effects mediated by the availability of different cues. In addition, we investigated how an Allee effect can influence movement and dispersal plasticity. 4. Our findings suggest that movement strategies in Tetrahymena are plastic and densitydependent. The observed movement reaction norm was U-shaped. This may be due to an Allee effect which led to negative density dependence at low population densities and generally positive density dependence at high population densities due to local competition. This possibly adaptive density-dependent movement strategy was likely mediated by chemical cues. 5. Our experimental work in highly controlled conditions indicates that both environmental cues as well as inherent population dynamics must be considered to understand movement and dispersal. Key-words: Allee effect, chemical cue, density-dependent dispersal, density-dependent movement, emigration, metapopulation, microcosm, movement, Tetrahymena

Introduction Dispersal is a central process for natural populations, as it links local populations to each other such that they form spatially structured populations (e.g. metapopulations; Hanski & Gaggiotti 2004; Fronhofer et al. 2012). Such a spatial structure may affect local population dynamics by preventing stochastic extinctions via rescue effects (Brown & Kodric-Brown 1977). Dispersal also is a key factor for community assembly and thus influences diversity patterns (Chave, Muller-Landau & Levin 2002; Nathan 2006). Finally, on a more macroscopic scale, dispersal, together with local adaptation, determines the

*Correspondence author. E-mail: [email protected]

geographical distribution of species (for a recent review on dispersal ecology and evolution and range dynamics see Kubisch et al. 2014). Therefore, understanding the causes and consequences of dispersal is an important aim in ecological and evolutionary research (Clobert et al. 2012). Dispersal comprises three more or less distinct phases: emigration, transition and immigration (Clobert et al. 2012). During all three phases, the acquisition, processing and use of external, internal and social information play an important role for the subsequent movement and dispersal decisions (Bowler & Benton 2005; Clobert et al. 2009). Natural selection will favour such conditiondependent movement and dispersal rules over uninformed strategies, as it gives individuals fitness advantages except if either the acquisition of information or the subsequent

© 2014 The Authors. Journal of Animal Ecology © 2014 British Ecological Society

2 E. A. Fronhofer, T. Kropf & F. Altermatt positive again at higher densities leading to a roughly U-shaped function (see Fig. 1). While these theoretical predictions are straightforward, empirical evidence is somewhat confusing and ambiguous. Positive density dependence has been found across many taxa (protists: Hauzy et al. 2007; rotifers: Kuefler, Avgar & Fryxell 2012; mites: Bitume et al. 2013; aquatic insects: Fonseca & Hart 1996; collembolans: Bengtsson, Hedlund & Rundgren 1994; spiders: De Meester & Bonte 2010; butterflies: Nowicki & Vrabec 2011; birds and mammals, for a review see: Matthysen 2005). However, also an overall negative density dependence has been reported across a similar diversity of organisms (protists: Fellous et al. 2012; and depending on genotypes Pennekamp et al. 2014; damselflies: Rouquette & Thompson 2007; butterflies: Baguette, Clobert & Schtickzelle 2011; black bears: Roy et al. 2012; birds and mammals, for a review see: Matthysen 2005). A noteworthy study has been conducted by Kim, Torres & Drummond (2009) who report a U-shaped density-dependent dispersal function,

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behavioural changes are too costly (Bowler & Benton 2005; Nathan et al. 2008; Clobert et al. 2009; Hovestadt, Kubisch & Poethke 2010). Possible sources of information are, for example, local conspecific density (Matthysen 2005; De Meester & Bonte 2010; Fellous et al. 2012; Bitume et al. 2013; Kuefler, Avgar & Fryxell 2013; Pennekamp et al. 2014), relatedness (Bitume et al. 2013), patch size (Crone, Doak & Pokki 2001; Altermatt , & Ebert 2008, 2010), the presence of other species (Hauzy et al. 2007) or food availability (Kuefler, Avgar & Fryxell 2012, 2013). Here, we focus on the effects of intraspecific density on movement strategies (density-dependent movement, DDM), because movement is the microscopic process from which dispersal emerges (see e.g. Nathan et al. 2008; Revilla & Wiegand 2008). Of course, movement behaviour is not exclusively a proxy for dispersal. For example, movement is also linked to foraging or mate-finding, reflecting spatial displacement without implying spatial gene flow. For the sake of simplicity, we will here focus on movement seen as the basis of dispersal. We understand density as the number of individuals relative to the carrying capacity and not relative to patch area or volume as the latter is not species-specific. Functional relationships capturing the effect of density on dispersal have been formally derived from first principles only for density-dependent emigration (DDE) by Metz & Gyllenberg (2001) for continuous-time systems and by Poethke & Hovestadt (2002) for discrete-time metapopulations (for ecological and evolutionary impacts of DDE see e.g. Amarasekare 2004; Hovestadt & Poethke 2006; Enfj€all & Leimar 2009; Travis et al. 2009; Kubisch, Poethke & Hovestadt 2011; Altwegg et al. 2013). The logic that emigration is selected for as long as the expected inclusive fitness of an emigrant is higher than the expected inclusive fitness of a resident individual leads to a threshold model: individuals should not emigrate as long as local population densities are low enough. Beyond this threshold, the functional relationship depends somewhat on the model assumptions, leading to a step function in continuous-time models (Metz & Gyllenberg 2001) or to a simple asymptotic function above the threshold for discrete-time models (Poethke & Hovestadt 2002). Similar ideas can be found in Ruxton & Rohani (1998) who have developed a model of fitness-dependent dispersal in metapopulations. In summary, emigration rate and population density (as a proxy for competition for any kind of resources) are fundamentally positively related. This relationship may be different for (very) small population sizes in species that suffer from an Allee effect. Allee effects are generally defined as a positive correlation between population density and individual fitness (Allee 1931; Courchamp, Berec & Gascoigne 2008). This leads to reduced fitness at small population densities which may be due to the lack of social interactions or reduced mating opportunities, for example. In such a scenario, DDE may have a negative slope at low densities but will become

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Population density [k] Fig. 1. Density-dependent emigration (DDE) in continuous-time (a) and discrete-time models (b) including an Allee effect. These relationships were derived by Metz & Gyllenberg (2001) for time continuous and by Poethke & Hovestadt (2002) for time discrete systems from first principles based on a marginal value approach (black lines). We added the most likely consequence of an Allee effect that was not included in the original DDE functions (grey lines). In contrast to DDE at high densities in discrete-time systems, we propose that an Allee effect should lead to a second threshold, as below this critical density threshold emigration should always be an ESS.

© 2014 The Authors. Journal of Animal Ecology © 2014 British Ecological Society, Journal of Animal Ecology

Density-dependent movement and Allee effects such as we describe above, in a colonial marine bird, the Blue-footed Booby. In addition to providing conflicting evidence about density-dependent dispersal, which may be due to different ranges of densities considered, most of these efforts concentrate uniquely on emigration strategies and do not analyse the underlying movement patterns (but see Kuefler, Avgar & Fryxell 2012, 2013). We here aimed at filling this gap by testing whether and how movement strategies (reaction norms; see Clobert et al. 2009) are plastic with respect to population density in organisms with an Allee effect. For our study, we used the model organism Tetrahymena, which is known to have an Allee effect (e.g. Christensen et al. 2001; Chaine et al. 2010). We used microcosm experiments (Jessup et al. 2004; Benton et al. 2007) because this approach allows us to carefully pinpoint the relevant cues, such as the (i) relative number of individuals, (ii) chemical cues or (iii) resource availability, used for DDM. In these tightly controlled experimental settings, we can individually manipulate these parameters and achieve a suitable level of replication. We addressed three questions: (i) Are movement strategies (characterized by velocity and the turning angle distribution) density-dependent and shaped by adaptation to an Allee effect? (ii) What proximate cues (i.e. relative number of individuals, chemical cues or resource availability) are used for density-dependent movement? (iii) How do these microscopic processes translate to the regional scale by affecting population spread (net distance travelled, diffusion coefficient)? We generally predict a U-shaped DDM function as an evolutionary consequence of the Allee effect (see also Fig. 1) as movement and dispersal were shown to correlate in Tetrahymena (Pennekamp 2014). Our detailed predictions regarding the influence of the three potential density cues (i.e. relative number of individuals, chemical cues or resource availability) on movement strategies are illustrated in Fig. 2. We always include a prediction for the case that a specific density cue is used in an adaptive way to mediate DDM as well as an alternative prediction for the case that this cue has concominant effects that cannot be interpreted as adaptive DDM.

Materials and methods study organism We used the freshwater protist Tetrahymena cf. pyriformis (Foissner pers. comm.; Simon, Nanney & Doerder 2008) as a model organism. This small ciliate (c. 35
5 lm along the major body axis under our laboratory conditions) exhibits high growth rates and carrying capacities (c. 2\r0 \4 per day and 6000\K\10000 per ml; see also Fig. 6a) which makes it an ideal study organism for answering ecological and evolutionary questions (e.g. Fjerdingstad et al. 2007; Hauzy et al. 2007; Schtickzelle et al. 2009; Altermatt, Schreiber & Holyoak 2011; Carrara et al. 2012; Giometto et al. 2014). Importantly, Tetrahymena species are known to suffer from an Allee effect (e.g., Christensen et al.

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2001). The resulting conspecific attraction made them a model organism for the study of cooperative behaviour (e.g. Schtickzelle et al. 2009; Chaine et al. 2010). We kept Tetrahymena in protist medium (Protozoan pellets; Carolina Biological Supply; 046 gl1 ) at a constant temperature of 22 ∘C (for a detailed description see Altermatt, Schreiber & Holyoak 2011; Carrara et al. 2012). Resources were supplied as 5% dense bacterial culture (c. 1 week old; Serratia fonticola, Bacillus subtilis and Brevibacillus brevis) per litre of protist medium.

microcosm experiments As described above, density-depend movement (DDM) can be mediated by three cues: (i) the relative number of individuals, (ii) chemical cues and (iii) resource availability. All three cues were manipulated separately while keeping the other two constant. All experiments were carried out in 15-ml tubes (Eppendorf, Hamburg, Germany) using a total of 1 ml protist medium and replicated five times (due to experimental failure one replicate had to be discarded from the experiment analysing the influence of the relative number of individuals). Measurements were taken 1 h after the application of the treatments. A gradient in cell densities was generated by diluting centrifuged cultures (see Fjerdingstad et al. 2007) of 5 days old populations of Tetrahymena. These cultures were assumed to be at carrying capacity (see Fig. 6a for a growth curve). Dilution yielded five levels of population densities (‘relative number of individuals’): 01, 05, 075, 1 and 15 times the carrying capacity. The carrying capacity (K) was estimated to be about 8600 individuals (see Fig. 6a). To keep resources and metabolites constant, we added 5% bacterial culture to all treatments and the dilution was carried out with filtered protist medium from the original cultures (filter pore size 02 lm). Resource content was manipulated by adding diluted bacterial cultures. This resulted in the following six levels of relative resource concentration (‘fraction bacterial culture’): 0, 0005, 0025, 005, 025 and 05. Tetrahymena metabolites (chemical cues) were kept constant by diluting the bacteria with fresh medium and by always using the same amount of Tetrahymena culture. The relative number of individuals was fixed to about half of the carrying capacity. Chemical cues were manipulated in analogy to the other two factors, namely by adding dilutions of filtered medium (filter pore size 02 lm) from a 3 weeks old Tetrahymena culture. We chose the following concentration levels (‘fraction old medium’): 0, 0005, 0025, 005, 025 and 05. We used old medium instead of directly adding possible chemical cues to fresh medium (as was done e.g. by Kovacs, Lovas & Csaba 1994) in order to guarantee that we were operating in a biologically plausible range of concentrations. This approach has been previously used by Fellous et al. (2012), for example. Evidently, we thereby loose some degree of control over the system and are not able to distinguish directly between the effects of different chemical compounds. To quantify the combined effect of all three possible cues on movement strategies as well as to obtain equilibrium densities and growth rates for our study species, we followed population growth over 4 days in six replicated populations grown in 20-ml vials (Sarstedt, Nümbrecht, Germany) with 15-ml medium. On day zero, these populations were inoculated with 1 ml of Tetrahymena taken from a batch culture. We fitted a logistic growth K function of the form NðtÞ ¼ with a ¼ lnð K  1Þ Nð0Þ 1 þ ear0 t

© 2014 The Authors. Journal of Animal Ecology © 2014 British Ecological Society, Journal of Animal Ecology

4 E. A. Fronhofer, T. Kropf & F. Altermatt

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Fig. 2. Qualitative predictions of density-dependent movement (DDM) reflecting the evolutionary consequences of an Allee effect and local competition. We predict (i) a concave up response for velocity (a, black) and a concave down response for the width of the turning angle distribution (a, grey) if the relative number of individuals (physical contacts) is used as a cue for DDM. This combination would lead to a U-shaped function for population spread (a, inset). However, a purely physical effect of crowding, leading to lower velocities and/or stronger turns as well as a decreasing net distance travelled, can also be predicted (b). (ii) Chemical cues (any substance secreted by the study organism) may be used to trigger DDM and should lead to the same U-shaped response as predicted for the relative number of individuals (c). Yet, such chemical cues may also have direct negative effects on Tetrahymena (Kovacs, Lovas & Csaba 1994) leading to less turns and slower movements (d). (iii) Trivially, low resource availability should trigger faster and straighter movement as an escape mechanism (e). As high resource availability is probably not a good indicator of low population densities, we do not predict a U-shaped reaction norm in this case. Clearly, the predictions depicted in (e) can also be interpreted as an effect of local foraging. Finally, a purely metabolic effect of resource availability (f) might allow faster movements and stronger turns if these are costly (Wilson et al. 2013). Higher velocities and more turns may cancel each other out resulting in a more or less flat relationship for displacement. In contrast to the relationships shown in Fig. 1, these functions are purely qualitative and not derived from first principles. Note that the location of the carrying capacity on the x-axes is of specific interest. Yet, as the exact shape of the reaction norms will depend on the costbenefit ratio of moving, which has to take into account movement costs or the mean expected inclusive fitness of individuals moving to new patches, for instance, we cannot exactly pinpoint the location of K. It should, however, roughly be located in the centre of the x-axes. © 2014 The Authors. Journal of Animal Ecology © 2014 British Ecological Society, Journal of Animal Ecology

Density-dependent movement and Allee effects where K is the carrying capacity and r0 is the growth rate using a nonlinear least squares approach (statistical software R; version 3.0.2, R Development Core Team 2013; function ‘nls’).

data collection After 1 h of treatment, the populations in the microcosms were sampled and we used video analysis to collect data on movement behaviour (velocities, turning angle distribution, net distance travelled, diffusion coefficient; see also Giometto et al. 2014). We followed the protocol proposed by Pennekamp & Schtickzelle (2013) using the free image analysis software IMAGEJ (version 1.46a U. S. National Institutes of Health, Bethesda, MD, USA, http://imagej.nih.gov/ij/) with the MOSAIC particle tracker plugin (Sbalzarini & Koumoutsakos 2005). Videos were recorded for 20 s (total of 500 frames) at a 30-fold magnification (imaged sample volume: 19 ll; height: 05 mm) using a Nikon SMZ1500 stereo-microscope (Nikon Corporation, Kanagawa, Japan) with a Hamamatsu Orca Flash 4 video camera (Hamamatsu Photonics K.K., Hamamatsu city, Japan). The image analysis first determines the location of moving particles of a pre-defined size range (determined through preliminary trials to be an area between 20 and 200 pixels) for every frame of the video by subtracting the information for two subsequent frames (‘difference image’). In a second step, these locations are relinked in order to obtain individual movement paths. For the linking procedure, we used the MOSAIC particle tracker plug-in. The algorithm is described in detail in Sbalzarini & Koumoutsakos (2005). In brief, the algorithm links particles identified in subsequent frames using a link distance (here set to 15 pixels). Linking can occur over more than two subsequent frames (here the relevant parameter is set to 3). The tracker plug-in allows for particles to disappear and if it is unable to infer a link the trajectory is terminated. For further details please also refer to the protocol described in detail by Pennekamp & Schtickzelle (2013).

statistical analysis The recorded movement paths allowed us to calculate descriptive indices of the movement behaviour such as velocity and circular standard deviation of the turning angle distribution as well as the net distance travelled, that is the Euclidean distance travelled. In order to obtain best estimates, we only included movement paths of individuals that could be observed during a minimum of a fifth of the total video time (4 s). We used the statistical software R (version 3.0.2; packages ‘adehabitatLT’ version 0.3.14 and ‘circular’ version 0.4-7; see also Pewsey, Neuh€auser & Ruxton 2013) to perform all analyses. In addition, we calculated the diffusion coefficient (i.e. the linear slope of mean square displacement over time) as a measure of population spread. The data can be downloaded from Dryad (Fronhofer, Kropf & Altermatt 2014). As Turchin (1998) noted, the turning angle distribution might suffer from autocorrelation due to oversampling of the movement path. In order to exclude any artefacts arising from our sampling method, we ran additional analyses with simplified movement paths. We only kept coordinates of the movement paths which were farther than a certain threshold (1, 2, 3, . . ., 25 pixels) from the straight line connecting the two locations surrounding it (for a detailed description see Pennekamp 2014). This was done using the Douglas–Peucker algorithm (statistical software R version 3.0.2; package ‘rgeos’ version 0.3-3, function ‘gSimplify’). We

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selected the minimal threshold for every movement path individually by iteratively increasing the threshold until no significant autocorrelation could be detected (package ‘adehabitatLT’ version 0.3.14 function ‘testang.ltraj’). The results of these analyses are reported in the Supporting information Fig. S1. Although the relationship between the width of the turning angle distribution and density was impacted by oversampling, it was not altered fundamentally. We chose to report the original, unmodified data in the main text as removing the autocorrelation also implies losing information about the biologically relevant autocorrelation. We analysed the individual level movement data (velocity, standard deviation of the turning angle distribution, net distance travelled) with linear mixed models or with generalized linear mixed models (in case assumptions of linear models were violated) using the statistical software R (version 3.0.2; functions ‘lmer’ and ‘glmer’ from the ‘lme4’ package version 1.0-4). In order to account for possible non-independence of individuals within one replicate, we used ‘replicate’ as a random effect. The analysis of the diffusion coefficient was carried out analogously with the difference that there was only one data point per replicate since the diffusion coefficient is a population level metric. We therefore did not include ‘replicate’ as a random effect and used linear models. After visual inspection, we either fitted linear, squared or cubed polynomials to the data and used AIC for model selection (optimizing the maximum likelihood criterion as we compare models with different fixed effects). We always added the null model for comparison and selected the best fitting model. This allowed us to infer the shape of population level reaction norms.

Results relative number of individuals Velocity was found to be independent of the relative number of individuals present [AIC(linear) = 1042044, AIC (null) = 1042183; Fig. 3a]. By contrast, the width of the turning angle distribution quantified as its standard deviation increased significantly with more individuals [AIC (linear) = 539287, AIC(null) = 534512; Fig. 3b]. These changes in the turning angle distribution led to an overall negative slope for the net distance travelled [AIC (linear) = 511341, AIC(null) = 518043; Fig. 3c; see Supporting information Fig. S2A for the diffusion coefficient and Fig. S3 for a plot with the measured densities on the x-axis].

chemical cues The relationship between movement strategies and chemical cues was clearly more complex (see Fig. 4); velocity was found to be a non-monotonic function of the concentration of chemical cues. While very small concentrations led to faster movements, the same was true for high concentrations (Fig. 4a). Yet, swimming speed decreased again for very high amounts of chemicals [AIC (cubic) = 493475, AIC(quadratic) = 491559, AIC(linear) = 48936, AIC(null) = 482919]. We observed the exact opposite pattern for the width of the turning angle

© 2014 The Authors. Journal of Animal Ecology © 2014 British Ecological Society, Journal of Animal Ecology

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Fig. 3. Effect of the relative number of individuals. The three panels depict the effect of conspecific density (measured relative to the carrying capacity, K) on movement strategies of Tetrahymena while keeping the two other possible cues (the amount of resources and the concentration of chemical cues) constant. Velocity was found to be independent of population density [LMM(null); N = 3716(4). As sample size N, we always report the total number of individuals and thereafter the number of replicates in brackets]. By contrast, we found a significantly negative relationship for the width (SD) of the turning angle distribution [GLMM(linear); N = 3716(4), error distribution family: Gamma]. These two aspects of movement taken together resulted in a negative slope for the net distance travelled, which is the Euclidean distance between the starting and the end point of an individual movement path [GLMM(linear); N = 3716(4), error distribution family: Gamma]. Note that the diffusion coefficient shows the same behaviour (Supporting information Fig. S2A). The grey circles indicate means and the error bars standard errors over the four replicates. The black squares and dotted lines are the model predictions. See Supporting information Fig. S3 for an analogous plot with the measured number of individuals on the x-axis.

distribution: straighter movements for low and high concentrations of chemical cues with a subsequent increase in turns for the highest value [AIC(cubic) = 246543, AIC (quadratic) = 242841, AIC(linear) = 238028, AIC (null) = 235805; Fig. 4b]. Taken together, these changes in velocity and movement straightness led to larger displacements at low and high concentrations of chemical cues and a drop in the distance covered for the highest concentration [AIC(cubic) = 255614, AIC(quadratic) =

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6 E. A. Fronhofer, T. Kropf & F. Altermatt

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Fig. 4. Effect of chemical cues. Chemical cues had a strongly nonlinear effect on movement strategies. While we observed a negative slope for velocity at low concentrations of chemical cues, this effect was inverted at higher concentrations. At the highest concentration, the slope became negative again [LMM(cubic); N = 1598(5)]. A similarly nonlinear correlation could be found for the width of the turning angle distribution. Yet, the slopes were exactly the opposite in comparison to velocity [LMM(cubic); N = 1598(5)]. This combination of fast and straight movement at low and high densities as well as slow movement and strong turns for intermediate and very high concentrations of chemical cues led to larger displacement distances (and diffusion coefficients; Supporting information Fig. S2B) for low and high concentrations [GLMM(cubic); N = 1598(5), error distribution family: Gamma]. The grey circles indicate means and the error bars standard errors over the five replicates. The black squares and dotted lines are the model predictions.

256252, AIC(linear) = 256816, AIC(null) = 257016; Fig. 4c; see Supporting information Fig. S2B for the diffusion coefficient].

resource availability Finally, we analysed the effect of resource availability on movement strategies (Fig. 5). We observed a significant increase in velocity at higher resource concentrations before a saturation was reached [AIC(quadratic) = 67757, AIC(linear) = 675776, AIC(null) = 66589; Fig. 5a]. A similarly positive relationship could

© 2014 The Authors. Journal of Animal Ecology © 2014 British Ecological Society, Journal of Animal Ecology

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concentrations, we additionally recorded movement patterns in non-manipulated, growing populations (Fig. 6). The growth curve (Fig. 6a) allowed us to estimated the carrying capacity to approximately K = 8600 individuals per ml and the growth rate r0 ¼ 4 per day. Over time – which here implied increasing population density,

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be found for the width of the turning angle distribution [AIC(linear) = 340666, AIC(null) = 339454; Fig. 5b]. This combination of slow but relatively straight movement for low resource concentrations and faster but less straight movement at high concentrations made the overall observed displacement not significantly related to resource availability [AIC(linear) = 289734, AIC (null) = 289705; Fig. 5c; see Supporting information Fig. S2C for the diffusion coefficient].

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Fig. 5. Effect of resource availability. We here explored the effect of resource concentration on movement behaviour and found a nonlinear positive correlation for velocity [LMM(quadratic); N = 2286(5)] and a linearly positive relationship for the width of the turning angle distribution [LMM(linear); N = 2286 (5)]. The interaction of increasing speed and decreasing straightness of the movement paths prevented net distance travelled (as well as the diffusion coefficient; Supporting information Fig. S2C) to correlate with resource availability [GLMM(linear); N = 2286(5), error distribution family: Gamma]. The grey circles indicate means and the error bars standard errors over the five replicates. The black squares and dotted lines are the model predictions.

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Fig. 6. Combined effect of all three cues in non-manipulated, growing populations of Tetrahymena. The top panel (a) shows the corresponding growth curve and allows the reader to relate time to density for panels b–d. We observed downwards U-shaped relationships between time, respectively populations density, and both velocity [b; LMM(cubic); N = 7757(6)] and the width of the turning angle distribution [c; LMM(cubic); N = 7757(6)]. The resulting net distance travelled showed an upwards U-shape [d; GLMM(cubic); N = 7757(6), error distribution family: Gamma]. The same pattern was observed for the diffusion coefficient (Supporting information Fig. S4). The grey inter-connected circles indicate the six replicates of growing populations. The black squares and lines are the model predictions.

© 2014 The Authors. Journal of Animal Ecology © 2014 British Ecological Society, Journal of Animal Ecology

8 E. A. Fronhofer, T. Kropf & F. Altermatt decreasing resource availability as well as an increasing concentration of chemical cues – both velocity [Fig. 6b; AIC(cubic) = 2330707, AIC(quadratic) = 2319438, AIC(linear) = 2287588, AIC(null) = 2102478] and the width of the turning angle distribution [Fig. 6c; AIC (cubic) = 1111395, AIC(quadratic) = 10977870, AIC (linear) = 1048871, AIC(null) = 970748] were downwards U-shaped. Together, these effects resulted in an upwards U-shaped relationship between net distance travelled and time, respectively population density [Fig. 6d; AIC(cubic) = 1211925, AIC(quadratic) = 1212021, AIC (linear) = 1214675, AIC(null) = 1220283; see Supporting information Fig. S4 for the diffusion coefficient).

Discussion Our experiments show that movement in Tetrahymena was plastic with regard to density. More specifically, we found evidence for a U-shaped relationship (Fig. 6) between movement and density. We speculate that this reaction norm is the signature of the evolutionary consequence of an Allee effect and of local competition. Furthermore, we tentatively suggest that in Tetrahymena, DDM is mediated by chemical cues (Figs 3–5).

relative number of individuals and resource availability The response elicited by the relative number of individuals (Fig. 3) corresponds to the prediction depicted in Fig. 2b. Although Tetrahymena did not show slower movements with increasing density, the width of the turning angle distribution increased significantly. Following our prediction, we interpret this as a physical effect of crowding: when more individuals are present, encounter rates increase and straight-line movements are less likely (Fig. 3b). Less straight-line movements were directly reflected in reduced displacement (Figs 3c and S2A). We suggest that the relative number of individuals is not used as a cue for DDM because negative DDM (or DDE) due to an Allee effect should be restricted to low densities as Allee effects only affect low-density populations. If resources are limited, competition will most likely lead to positive DDM and DDE at higher densities (Metz & Gyllenberg 2001; Poethke & Hovestadt 2002). Of course, the slope will depend on the cost-benefit calculation that takes into account the strength of local competition, movement and dispersal costs (Bonte et al. 2012) and the expected inclusive fitness of the emigrant. The plastic response we observed in relation to the amount of resources available (Fig. 5) is best explained by metabolic effects of increased energy availability, probably also by foraging behaviour and not by DDM. As predicted in Fig. 2f velocity increased with increasing resource availability (Fig. 5a). This is contrary to what we had expected if resources were used as a cue for DDM, as lower resource concentrations can be interpreted as

increased competition which should trigger emigration (Fig. 2e). At the same time, we observed an increased occurrence of turns in the movement paths (Fig. 5b). This can be interpreted in two ways, which are not mutually exclusive: (i) If turns are costly (Wilson et al. 2013), more resources will allow individuals to perform more turns. (ii) Alternatively, more turns can be an emergent phenomenon of more or less systematic search behaviour for food in resource-rich environments (see Kareiva & Odell 1987; and Benhamou 1992; for area-restricted search strategies; Fronhofer, Hovestadt & Poethke 2013; for non-random within patch search). Displacement was not affected by the amount of resources present (Figs 5c and S2C) as the effects of faster and less straight movements cancel each other out.

chemical cues potentially mediate densitydependent movement The results we obtained for chemical cues (Fig. 4) correspond to our predictions for DDM (Fig. 2c), except for the highest concentration. We observed fast and straight movements at very low as well as at high concentrations of chemical cues (Fig. 4a and b). We suggest that this led to negative DDM for low and positive DDM for high concentrations, respectively (Figs 4c and S2B). Although we did not determine the chemical composition of the ‘old’ medium we used for these experiments, we can formulate an educated guess about possibly important compounds, which can be used as cues for population density, based on biomedical studies that use Tetrahymena as a model organism (e.g. Rasmussen et al. 1996; Rasmussen & Rasmussen 2000; Christensen et al. 2001; Csaba 2012). Cell death at low population densities (Allee effect) is most likely regulated through intracellular signalling, as low-density populations can be rescued by the addition of cGMP or protein kinase activators. The addition of low concentrations of insulin (1014 to 1011 M) had comparable effects which suggests that insulinmediated signal transduction pathways are involved (for a review see e.g. Rasmussen et al. 1996). Note that although most of these studies were performed with Tetrahymena thermophila the findings are very likely applicable not only to other Tetrahymena species but also to a wide range of other unicellular eukaryotes (Christensen et al. 1997). The decrease in velocity and net distance travelled we observed at the highest concentration of chemical cues (Fig. 4) is consistent with previous studies (Kovacs, Lovas & Csaba 1994; these authors used concentrations of 106 M vs. 1014 to 1011 M used to rescue cells at low densities) and is probably due to a negative effect of high concentrations of metabolites such as insulin on swimming speed (as depicted in Fig. 2d). Based on these interpretations and our predictions (illustrated in Fig. 2), we hypothesize that such chemical compounds (or the lack thereof) can reliably indicate local

© 2014 The Authors. Journal of Animal Ecology © 2014 British Ecological Society, Journal of Animal Ecology

Density-dependent movement and Allee effects population density, which is not the case for resource availability, for example. Chemical cues may also be less costly for estimating the presence and abundance of conspecifics, rather than perceiving the relative number of actively moving organisms directly. Note that these conclusions strongly depend on the cubic fit we observe in Fig. 4 which is determined by the values observed for one concentration (025). In addition, the general value of chemical cues for eliciting density-dependent behaviour remains to be established as Fellous et al. (2012), for example, found no effect of such metabolites on emigration behaviour in the freshwater protozoan Paramecium caudatum. While the lack of a statistical relationship in the latter study may not necessarily reflect the absence of an effect in general, it nevertheless shows that the detection might depend on the specific experimental set-up. Our results are consistent with previous work by Hauzy et al. (2007) on predator-induced dispersal who found that chemicals emitted by predatory protists were used as a cue for emigration in Tetrahymena. We are confident that an analogous mechanism can be relevant to sense intraspecific density.

allee effects and local competition likely shape the reaction norm In the light of our predictions (Figs 1 and 2), we speculate that the U-shaped DDM reaction norm reported in Fig. 6 results from the interaction of the Allee effect and local competition: Reduced fitness at both low and high population densities has the potential to select for movement and dispersal as a means to escape from these conditions. Our results suggest that the width of the turning angle distribution is a major determinant of displacement in Tetrahymena. The downwards U-shape we observed reflects the pattern measured for chemical cues alone (Fig. 4b) without the effect of very high concentrations. This is not surprising since the culture used as a donor of chemical cues in Fig. 4 was more than three times as old as the cultures in Fig. 6. We here cannot exclude that the relative number of individuals (Fig. 3) plays a role as a cue for negative DDM at low densities (Fig. 6; note the different x-axes when comparing Figs 3, 4 and 6). Yet, as the width of the turning angle distribution decreases again for densities approaching carrying capacity (Fig. 6c), we suggest that chemical cues are more relevant, at least at high population densities. We assume that the shape of the curve for velocity (Fig. 6b) is influenced by an interaction between chemical cues and high resource availability, which might have increased velocity overall (compare the y-axes of Figs 4 and 6) and decreased the relative difference between the first values. Nevertheless, the net distance travelled (Fig. 6d) clearly shows the predicted U-shaped relationship for DDM (and DDE, if one assumes a simple scaling) in species with an Allee effect.

9

Comparisons and conclusions Our findings are in good accordance with recent work by Kuefler, Avgar & Fryxell (2012) who showed that diffusion is positively density-dependent in a rotifer species. Here, we did not consider the internal state of our study organism but were interested in a more mechanistic analysis of the external factors, such as density and relevant cues, and relating them in full detail to three aspects of the movement path: velocity, turning angle distribution and displacement. This allowed us to interpret the negative relationship reported in the experiment in which we manipulated the relative number of individuals as an effect of crowding. Similarly, Kuefler, Avgar & Fryxell (2013) analysed the impact of resource concentration and conspecific density. They could show that the presence of resources increased the number of turns in a one-dimensional landscape, indicating that the presence of competitors affected velocity, which then led to more displacement. The reaction norms we measured confirm these findings, except for the effect of resources on velocity which is inverted here. We suggest that this is due to a positive metabolic effect linked to resource intake and that our study organisms were more resource limited. In conclusion, our study allows us to tentatively generalize DDM (and by extension DDE) to organisms that have an Allee effect (for examples see Courchamp, Berec & Gascoigne 2008). In this light, our experiments (especially Fig. 6d) are a confirmation of the hypothesis expressed by Kim, Torres & Drummond (2009) who provided first correlational evidence that dispersal propensity follows a U-shaped function in species with an Allee effect. This suggests that discussions about whether DDE or DDM exhibit globally positive or negative slopes might be misleading, as both conditions can be found in U-shaped reaction norms, depending on whether data were collected for generally low or high densities.

Acknowledgements We would like to thank two anonymous referees for their valuable comments that helped us improve our work a lot and Frank Pennekamp for his input concerning data analysis. We would also like to thank Pravin Ganesanandamoorthy for help with data collection. E.A.F. thanks the Eawag for funding. Funding to F.A. was provided by the Swiss National Science Foundation, grant nr. 31003A_135622 and PP00P3_150698.

Data accessibility Data available from the Dryad Digital Repository: http://doi.org/10.5061/ dryad.383q4 (Fronhofer et al. 2014).

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Supporting Information Additional Supporting Information may be found in the online version of this article. Fig. S1. Width of the turning angle distribution with simplified paths. Fig. S2. The diffusion coefficient. Fig. S3. The effect of the relative number of individuals. Fig. S4. The combined effect of all three cues in non-manipulated, growing populations of Tetrahymena on the diffusion coefficient.

© 2014 The Authors. Journal of Animal Ecology © 2014 British Ecological Society, Journal of Animal Ecology